非线性热传导方程的Lagrange插值逼近  

Lagrange Interpolation Approximation of Nonlinear Heat Transfer

作　　者：王天军[1] 贾丽蕊[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2011年第2期68-71,111,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(10871131);河南科技大学博士启动基金项目(09001263);河南科技大学SRTP基金项目(2009179)

摘　　要：利用Legendre-Gauss-Lobatto节点为插值节点,构造Lagrange插值多项式,作为基函数展开问题的数值解,逼近有界杆上的非线性热传导方程Neumann边值问题的正确解。给出算法格式和相应的数值例子,表明所提算法格式的有效性和高精度。所给算法也可用于求解其他非线性问题的Neumann边值问题。This paper deals with the numerical solutions of the nonlinear heat transfer with Neumann boundary condition on bounded interval.Legendre-Gauss-Lobatto nodes were used to construct the Nth degree Lagrange interpolation polynomial to approximate the solution of the nonlinear heat transfer with Neumann boundary condition.Efficient algorithms was implemented.Numerical results demonstrate its efficiency and high accuracy of this approach.Especially,it is much easier to deal with nonlinear heat transfer.The proposed method is also applicable to other nonlinear problems defined on certain bounded domains.

关 键 词：非线性热传导方程 Legendre-Gauss-Lobatto节点 Lagrange插值逼近 NEUMANN边值问题 

分 类 号：O175.2[理学—数学]